Studies of decision making in animals suggest a neural mechanism of evidence accumulation for competing percepts according to Bayesian sequential analysis. This model of perception is embodied here in a biomimetic tactile sensing robot based on the rodent whisker system. We implement simultaneous perception of object shape and location using two psychological test paradigms: first, a free-response paradigm in which the agent decides when to respond, implemented with Bayesian sequential analysis; and second an interrogative paradigm in which the agent responds after a fixed interval, implemented with maximum likelihood estimation. A benefit of free-response Bayesian perception is that it allows tuning of reaction speed against accuracy. In addition, we find that large gains in decision performance are achieved with unforced responses that allow null decisions on ambiguous data. Therefore free-response Bayesian perception offers benefits for artificial systems that make them more animal-like in behavior.